If they are the BBWs about 24" should do it, once they get over their "SkyKing" phase.
If you have heritage birds then it doesn't matter how tall you make it, you will need to put some type of cover on it. I have seen my BR hens go over a 12' wall. Really impressive.

I would keep them contained. Just for their own safety. You wouldn't believe what they can get into left to their own devices.
As to running chickens with them, I don't do it. A lot of people do, but be aware of the risks such as blackhead and the fights.